Stability analysis on the kerosene nanofluid flow with hybrid zinc/aluminum-oxide (ZnO-Al2O3) nanoparticles under Lorentz force

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
LiJun Zhang ◽  
Tayyaba Nazar ◽  
M.M. Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Aluminum Oxide ◽  
Dual Solutions ◽  
Graphical Form ◽  
Al2o3 Nanoparticles ◽  
Lower Branch ◽  
Suction Parameter ◽  
Content Type ◽  
Zinc Aluminum Oxide

Purpose The flow and heat transfer of a hybrid nanofluid composed of kerosene and ZnO-Al2O3 nanoparticles (NPs) is investigated. The flow occurs over complex surfaces with stretching and shrinking features. The base fluid is electrically conducting, and an external magnetic field is added so that the nanofluid and the electric field are in equilibrium. Irrotational flow with viscous dissipation effects is considered. Design/methodology/approach The governing equations of the system are formulated, and a similarity transformation is used to convert the system of equations into ordinary differential equations, which are solved numerically. The friction coefficient of the flow and the Nusselt number are calculated for a wide range of parameters, and the results are presented in graphical form. In addition, dual solutions of the problem were noticed to occur for a certain range of the unsteadiness parameter. A stability analysis has been performed and presented to elucidate the behavior of these dual solutions. Findings For the solution of the upper branch, the velocity and temperature profiles of the nanofluid are enhanced by increasing the magnetic field parameter M, but the same variables decrease in the solution of the lower branch. The same trend is detected for the velocity of the fluid with the suction parameter. The temperature of the nanofluid decreases in both branches of the solution by increasing the Prandtl number. Similarly, they decrease with the suction parameter. The temperature of the nanofluid slightly increases in both branches of the solution by increasing the Eckert number. With the stability analysis the authors performed, it was determined that the solution is stable in the upper branch, but unstable in the lower branch. Originality/value The kerosene nanofluid with hybrid Zinc/Aluminum-oxide is presented for the first time in the literature.

Additional results for the problem of MHD boundary-layer flow past a stretching/shrinking surface

2016 ◽  
Vol 26 (7) ◽  
pp. 2283-2294 ◽  
Author(s):  
Ioan Pop ◽  
Natalia C. Roşca ◽  
Alin V. Roşca
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Layer Flow ◽  
Similarity Solutions ◽  
Lower Solution ◽  
Dual Solutions ◽  
Suction Parameter ◽  
Content Type ◽  
Layer Flow ◽  
The Stability

Purpose The purpose of this paper is to reinvestigate the problem of multiple similarity solutions of the two-dimensional magnetohydrodynamic boundary-layer flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking permeable surface studied by Aly et al. (2007). Design/methodology/approach The transformed ordinary (similarity) differential equation was solved numerically using the function bvp4c from MATLAB. The relative tolerance was set to 10^(−10). Findings Dual solutions were found and a stability analysis was performed to show which solutions are stable and which are not stable. On the other hand, Aly et al. (2007) have shown that for each value of the power index and magnetic parameter in the range and for any specific values of the stretching/shrinking parameter and suction parameter the problem has only a solution. Originality/value The paper describes how multiple (dual) solutions for the flow reversals were obtained. The stability analysis has shown that the lower solution branches are unstable, while the upper solution branches are stable.

Analysis of Hiemenz flow of Reiner-Rivlin fluid over a stretching/shrinking sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Golam Mortuja Sarkar ◽  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Friction Coefficient ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Hiemenz Flow ◽  
Self Similar ◽  
The Stability

Purpose This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet. Design/methodology/approach The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable. Findings It is observed that the self-similar equations exhibit dual solutions within the range [λc, −1] of shrinking parameter λ, where λc is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain. Originality/value This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid Nanofluid: Stability analysis for dual solutions

2022 ◽  
pp. 239779142110690
Author(s):  
Seema Tinker ◽  
SR Mishra ◽  
PK Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Dual Solutions ◽  
The Other ◽  
Time Dependent ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Heat Transfer Characteristics ◽  
Suction Parameter ◽  
Transfer Characteristics

The heat transfer characteristics for the flow of a time-dependent hybrid nanofluid with thermal radiation and source/sink over a stretching/shrinking sheet are examined in the current investigation. We have transformed the governing equations of the presented study into the similarity equations utilizing similarity variables. However, a numerical solution is obtained by using in-build MATLAB code bvp5c. The mass and energy profiles for diverse values of thermophysical parameters are studied together with their physical quantities. It is observed that dual solutions exist, that is, one is upper, and the other is lower branch solution for a definite choice of the unsteadiness parameter. Also, stability analysis is executed to determine the long-term stability of dual solutions, indicating that out of the two, only one is stable and the other is unstable. It is revealed that comparatively, the first solution shows stability, while the second solution shows instability. There is a considerable influence of second-order slip on the problem’s respective flow and heat transfer characteristics. Further, major outcomes also show the dimensionless frictional stress and the magnitude of conventional heat transfer enhancement with growing suction parameter values.

Numerical solutions for unsteady boundary layer flow of a dusty fluid past a permeable stretching/shrinking surface with particulate viscous effect

2018 ◽  
Vol 28 (6) ◽  
pp. 1374-1391 ◽  
Author(s):  
Rohana Abdul Hamid ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Fluid Particle ◽  
Dust Particles ◽  
Physical Parameters ◽  
Suction Parameter ◽  
Content Type ◽  
Dusty Fluid ◽  
Wide Range

Purpose This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface. Design/methodology/approach The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software. Findings The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable. Practical implications In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials. Originality/value Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

scholarly journals MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field

2019 ◽  
Vol 30 (11) ◽  
pp. 4697-4710 ◽  
Author(s):  
Fadzilah Md Ali ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Convection Boundary Layer ◽  
Induced Magnetic Field ◽  
Content Type ◽  
The Stability

Purpose This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics. Originality/value The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

Linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles: application to controlled drug delivery

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Cédric Gervais Njingang Ketchate ◽  
Didier Fokwa ◽  
Ghislain Tchuen
Keyword(s):  
Magnetic Field ◽  
Drug Delivery ◽  
Stability Analysis ◽  
Magnetic Nanoparticles ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Controlled Drug Delivery ◽  
Darcy Number ◽  
Content Type ◽  
The Stability

Purpose For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery. Design/methodology/approach Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field. Findings It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force. Originality/value The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

Instability of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Cédric Gervais Njingang Ketchate ◽  
DIdier Fokwa ◽  
Ghislain Tchuen
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Porous Media ◽  
Stability Analysis ◽  
Volume Fraction ◽  
Temporal Stability ◽  
Darcy Number ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
The Magnetic Field

Purpose This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion. Design/methodology/approach The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al2O3) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed. Findings It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability. Originality/value The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.

scholarly journals Numerical and Computer Simulations of Cross-Flow in the Streamwise Direction through a Moving Surface Comprising the Significant Impacts of Viscous Dissipation and Magnetic Fields: Stability Analysis and Dual Solutions

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yu-Ming Chu ◽  
Umair Khan ◽  
A. Zaib ◽  
S. H. A. M. Shah ◽  
Marin Marin
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Cross Flow ◽  
Dual Solutions ◽  
Lower Branch ◽  
Suction Parameter ◽  
Highly Nonlinear ◽  
Branch Solution ◽  
Flow Through ◽  
The Impact

The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discussed with the help of plots. Dual solutions are obtained for certain values of a moving parameter. The velocities in the direction of streamwise, as well as cross-flow, decline in the upper branch solution, while the contrary impact is seen in the lower branch solution. However, the influence of suction on the velocities in both directions uplifts in the upper branch solution and shrinks in the lower branch solution. The analysis is also performed in terms of stability to inspect which solution is stable or unstable, and it is observed that the lower branch solution is unstable, whereas the upper branch one is stable.

The effect of vertical throughflow on the boundary layer flow of a nanofluid past a stretching/shrinking sheet

2017 ◽  
Vol 27 (9) ◽  
pp. 1910-1927 ◽  
Author(s):  
Ioan Pop ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Anuar Ishak
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Vertical Throughflow ◽  
Layer Flow

Purpose The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

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